A global prescribed performance control method is proposed for a class of uncertain high-order odd-rational-power nonlinear systems (a chain of integrators whose power is the ratio of odd integers) with actuator faults, where the high-order odd-rational powers and the parameters of actuator faults are unknown. A new coordinate transformation on the state and tracking errors is introduced based on the tangent function and its inverse function, resulting in a global low-complexity prescribed performance controller. The proposed controller does not require any knowledge of system nonlinearities or powers, and it also does not require the time derivatives of virtual control signals without using any filters, which implies the controller is of low complexity. Finally, two simulation examples, including a practical high-maneuver flight control example, are given to demonstrate the effectiveness of our method.